Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C22⋊C4×S4 |
| Fitting | C22×C22⋊C4 ⋊ D3 |
657 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 12 points:
(9,10,12,11);(6,8)(10,11,12);(1,2,3,4)(5,6)(7,8)50 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#99, C2×C22⋊C4×S4, S4×#117, … |
| maximal normal subgroup of | S4×#99, C2×C22⋊C4×S4, S4×#117, … |
| maximal quotient of | C22⋊C4×SL(2,ℤ/4), S4×#95, #11711692, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17871);